Related papers: Some improvements to product formula circuits for …
We devise a quantum-circuit algorithm to solve the ground state and ground energy of artificial graphene. The algorithm implements a Trotterized adiabatic evolution from a purely tight-binding Hamiltonian to one including kinetic,…
Generating large, non-trivial quantum chemistry test problems with known ground-state solutions remains a core challenge for benchmarking electronic structure methods. Inspired by planted-solution techniques from combinatorial optimization,…
Quantum computers offer the potential to efficiently simulate the dynamics of quantum systems, a task whose difficulty scales exponentially with system size on classical devices. To assess the potential for near-term quantum computers to…
Digital quantum simulation relies on Trotterization to discretize time evolution into elementary quantum gates. On current quantum processors with notable gate imperfections, there is a critical tradeoff between improved accuracy for finer…
Unwanted interaction between a quantum system and its fluctuating environment leads to decoherence and is the primary obstacle to establishing a scalable quantum information processing architecture. Strategies such as environmental and…
We investigate the quantum algorithm of Babbush et al. (arXiv:2303.13012v3) for simulating coupled harmonic oscillators, which promises exponential speedups over classical methods. Focusing on linearly connected oscillator chains, we bridge…
We consider the problem of learning the Hamiltonian of a quantum system from estimates of Gibbs-state expectation values. Various methods for achieving this task were proposed recently, both from a practical and theoretical point of view.…
We present the meta-VQE, an algorithm capable to learn the ground state energy profile of a parametrized Hamiltonian. By training the meta-VQE with a few data points, it delivers an initial circuit parametrization that can be used to…
The work presents a simple formalism which proposes an estimate of the ground state energy from a single reference function. It is based on a perturbative expansion but leads to non linear coupled equations. It can be viewed as well as a…
Electronic structure simulation is an anticipated application for quantum computers. Due to high-dimensional quantum entanglement in strongly correlated systems, the quantum resources required to perform such simulations are far beyond the…
Quantum algorithms for probing ground-state properties of quantum systems require good initial states. Projection-based methods such as eigenvalue filtering rely on inputs that have a significant overlap with the low-energy subspace, which…
We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of…
Quantum algorithms for diverse problems, including search and optimization problems, require the implementation of a reflection operator over a target state. Commonly, such reflections are approximately implemented using phase estimation.…
Quantum simulation is a foundational application for quantum computers, projected to offer insights into complex quantum systems beyond the reach of classical computation. However, with the exception of Trotter-based methods, which suffer…
We introduce an algorithm to improve the error scaling of product formulas by randomly sampling the generator of their exact error unitary. Our approach takes an arbitrary product formula of time $t$, $S_k(t)$ with error $O(t^{k+1})$ and…
In this work we investigate methods to improve the efficiency and scalability of quantum algorithms for quantum chemistry applications. We propose a transformation of the electronic structure Hamiltonian in the second quantization framework…
We propose a class of randomized quantum Krylov diagonalization (rQKD) algorithms capable of solving the eigenstate estimation problem with modest quantum resource requirements. Compared to previous real-time evolution quantum Krylov…
We present a novel method for improving the quantum simulation of the ground state energy of molecules. We perform a pre-processing step classically, which reduces the dimensionality of the problem by generating a custom mapping which…
We propose a quantum inverse iteration algorithm which can be used to estimate the ground state properties of a programmable quantum device. The method relies on the inverse power iteration technique, where the sequential application of the…
A new efficient numerical algorithm for interacting fermion systems is proposed and examined in detail. The ground state is expressed approximately by a linear combination of numerically chosen basis states in a truncated Hilbert space. Two…